stiffness method

1. PREPARED BY : )
GUIDED BY: -GUIDED BY: -

2. What is indeterminate structure?
 The structure which can not be analysed by the equations of
static equilibriums alone are called indeterminate structures.
 This kind of structure consist of more members and more
restraints.

3. Why Stiffness Method should use
The ability to automate the solution process.
Implementation in a computer program is possible.

4. Stiffness method is used for solving
problems related with,
 Beams
 Frames
 Trusses

5. Stiffness Method:
The stiffness method is defined as the end moment required to
produce a unit rotation at one end of the member while the
other end is fixed.
Degree Of Freedom (DOF):
Number of directions that the joints can move.

6. Degree of freedom for different
structural system
Structure Type Translational Rotational Total
Beam 1 1 2
Plane Truss 2 0 2
Plane Frame 2 1 3

7. Degree of Kinematic Indeterminacy (DOKI):
Total number of degree of freedom of the structure.
i.e. degree of freedom at all the joints less than no of restraints at
supports.
DOKI=(Number of joints)*(Number of DOF/joints)-Number
of restraints.

8. The steps to be followed in performing
a stiffness analysis can be summarized as:
I. Determine degree of kinematic indeterminacy.
II. Apply restraints and make it kinematically determine.

9. III. Apply loads on the fully restraint structure and calculate forces.
IV. Apply unknown displacement to the structure one at a time
keeping all other displacements zero and calculate forces
corresponding to each degree of freedom.

11. V. Equilibrium equations are written and solved
in matrix form and obtain the value of
unknown displacements.
VI. All the member-end forces are calculated.

12. Equilibrium equation:
Pm+Ku=Pj
Here,
Pm=Member force Matrix
K=Stiffness Matrix
u=Unknown displacement
Pj=Joint Load Matrix

14. EXAMPLES

15. Formulate the stiffness matrix for
a beam shown with co-ordinates in
fig

31. Thank you